Impulsively Reflected Ions: A New Theory for Ion Acoustic Wave Growth in Collisionless Shocks K. A. Goodrich, R. E. Ergun, S. J. Schwartz, L. B. Wilson III and the MMS Team

Shocks Convert Kinetic Energy to Thermal Energy… But How? Collisionless Shocks Rankine-Hugoniot Conditions: mass in = mass out momentum in = momentum out energy in = energy out* *We do not know exactly how energy is converted in the shock ??? Energy can be converted in many ways: Turbulence Particle Reflection Other Nonlinear Processes But this part is hard to observe

Why We Need E Field at Shocks McFadden et al., [2008] Shock THEMIS ~80 minutes ~3 second Particle time resolution Only a few data points of particle data during actual shock For physics inside the shock, we often need E field (kSamples/s)

The Bow Shock has a LOT of Wave Activity MMS ~9 min 0.03/0.15 ms e/ion resolution EM Whistler Waves Magnetosonic Waves < 100 Hz Up to 700 mV/m! Large Amplitude E *(that’s really high!) Electrostatic noise 100 Hz to kHz

Electrostatic Noise = Even More Waves Electrostatic Solitary Waves Electron Bernstein Waves Ion Acoustic Waves

Electrostatic Noise = Even More Waves Electrostatic Solitary Waves Electron Bernstein Waves Ion Acoustic Waves We’re going to focus on IAWs

Propagate obliquely to B Can have very high amplitudes (> 100 mV/m Wilson et al., [2014] Fuselier and Gurnett, [1984] Ion Acoustic Waves (IAWs) are frequently observed in the terrestrial bow shock and foreshock Short wavelength (~100 m) Propagate obliquely to B Can have very high amplitudes (> 100 mV/m Balikhin et al., [2005]

The Problem with IAWs IAWs are frequently observed in the bow shock But no one really knows why… Theoretically IAWs are generated by Current instabilities Ion-ion counterstreaming But both require a high Te/Ti ratio > 3 This rarely happens at the bow shock Some processes can reduce Te/Ti But we haven’t been able to observe them!

Observations: Shock Event MA ~ 11 β ~ 3 Solar Wind Te/Ti ~ 2

Observations: Shock Event B: Turbulent B: Steady E: Many wave modes E: Mostly IAWs SW Speed: Strong deceleration localized acceleration SW Speed: Slight deceleration!

Observations: Shock Event B: Turbulent B: Steady E: Many wave modes E: Mostly IAWs SW Speed: Strong deceleration localized acceleration SW Speed: Slight deceleration!

Observations: Shock Event B: Turbulent B: Steady E: Many wave modes For more details on this event: Goodrich, K. A., et al. (2018). MMS observations of electrostatic waves in an oblique shock crossing. Journal of Geophysical Research: Space Physics, 123. https://doi.org/10.1029/2018JA025830 E: Mostly IAWs SW Speed: Strong deceleration localized acceleration SW Speed: Slight deceleration!

Observations: Ion Acoustic Waves Seen with reflected ions (not currents) Short wavelength (< 200 m) Frequency at fpi fpi ~ 1 kHz Short durations 10 -100 ms Broadband spectral signatures Propagates obliquely to B B E REF SW Speed

Observations: Ion Distributions ~6 seconds Large variations between 150 ms distributions Consistent with ion beams .75 sec *f(V) Integrated along vector of least difference between SW and reflected ions

Theory and Analysis: Fried-Conte Solver SW R H To see if IAWs can be generated we… Break up 1D distribution into series of Maxwellians Solar Wind Reflected Ions Hot Cloud electrons (not shown) Use Maxwellians to derive longitudinal dielectric function 3) When 0 waves can exist χ = susceptibility of each Maxwellian

Theory and Analysis: Unaltered Distribution No waves!

Theory and Analysis: Added Beam Half-Maxwellian proxy for impulsive burst of reflected ions Two roots ϵ =0 Waves!

Theory and Analysis: Added Beam Unstable to Waves with… f ~ 1 kHz (close to fpi) λ~250 m (close to observed λ)

Observations vs Model Observations Model - < 100 mV/m λ ~ 250 m f ~ 1 kHz (fpi) unclear how long these waves persist < 100 mV/m λ < 200 m f ~ 1 kHz (fpi) observed between 10 and 100 ms

Implications Need a very strong positive slope to create instability That slope can erode very quickly from... Slower ions filling in the distribution Ion reflection can happen at various points throughout the shock Quasilinear diffusion Slows reflected ions May also decelerate solar wind ions!

Conclusions MMS observes IAWs in an oblique shock IAWs likely caused by ion-ion counterstreaming Te/Ti too low to allow IAW generation Short time-scale variations seen in ion distribution functions Fried-Conte analysis shows dispersive ion bursts can allow IAW generation. Waves may be quickly damped due to Slower moving ions Quasilinear diffusion Suggests ions can be impulsively reflected at various points of the shock. IAWs may also serve as a secondary method of solar wind deceleration